Question

Prove that a straight line add up to 180 degree

Answer 1

нєℓℓσ ∂єαя υѕєя!!


нєяє ιѕ уσυя αиѕωєя тнαт уσυя ωαιтιиg fσя....


αиѕωєя:

=>When we draw a circle whose center is on a straight line the circle is divided into two equal semi-circles.

=>The total degree of a circle is by definition 360 degrees.

=>Thus each semi circle accounts for 180 degrees.

=>That is the central angle is also 180 degrees.....

=>Thus the straight line add up to 180 degrees.....



ι нσρє тнιѕ ωιℓℓ нєℓρ уσυ συт



нανє α gяєαт ∂αу αнєα∂...... :)



•_•

Answer 2

Hey there!

Prove that a straight line add up to 180 degree

$\underline {Linear Pair Axiom}$ : According to this, If a ray stands on a line, sum of two adjacent angles formed is 180°

$\textbf {Proof}$

(Refer Figure)

Given,

A ray CD stands on line AB
forming ∠ACD = ∠BCD

To prove : ∠ACD + ∠BCD = 180°

Construction : Draw ray CE ⟂ AB

Proof :
∠ACD = ∠ACE + ∠ECD ----(i)
∠BCD = ∠BCE - ∠ECD ------(ii)

Adding (i) and (ii)

∠ACD + ∠BCD =∠ACE + ∠ECD + ∠BCE - ∠ECD

∠ACD + ∠BCD = ∠ACE + ∠BCE

∠ACD + ∠BCD = 90° + 90° = 180°
(since ∠ACE and ∠BCE = 90°)

Hence, Proved.

Hope it helps!!